Robust minimum entropy tracking control with guaranteed stability for nonlinear stochastic systems under modeling errors

In this paper, robust minimum entropy tracking control problem is considered for nonlinear stochastic systems. The controlled systems are described by nonlinear non-Gaussian difference equations with the un-modeled uncertainty and modeling error, as well as time delays. Entropy is adopted to characterize the uncertainty of the tracking error. The nonlinear multi-step-ahead predictive cost function is used and the relationship between the probability density functions of the input and the tracking error via the uncertain mapping is established. With these formulations, the cost function can be bounded as a nonlinear functional of the control input and the known bounds of the errors. Explicit design algorithms are presented for the robust suboptimal controller and further for the stabilization controllers. The Renyi's entropy has also been used to simplify the cost function. Simulations are given to demonstrate the effectiveness of the proposed control algorithm.